I have never heard of being able to hire out PC's before. I guess by the lack of responses no one really has.
Depending on what you are looking for and for what duration, maybe something like EBay might sell some Ok machines to you, that you could then sell on again later. You might lose some cash but hey, you were going to pay to hire anyway...
If you're in or near west London, there's an independent small computer business in Fulham that thinks slightly outside the box and might be worth talking to. I can't remember the name but if you want to follow up I'll check it.
Speaking of West London, a couple of years ago there was a daily computer fair in Queensway (edge of Kensington Park) and there was a guy there who rented out PCs by the day. There may be something there now.